A058475 Total number of interior nodes in all series-parallel networks with n labeled edges, multiple edges not allowed.

0, 0, 1, 5, 41, 394, 4704, 65386, 1049754, 19032392, 385419072, 8615947592, 210831826952, 5604404196832, 160834760288864, 4955867959526784, 163197046787269792, 5719576163352685696, 212565832527352216928, 8350117027586731306848

Offset: 0

Author

N. J. A. Sloane, Dec 20 2000

Keywords

• nonn
• nice
• easy

References

• J. W. Moon, Some enumerative results on series-parallel networks, Annals Discrete Math., 33 (1987), 199-226 (the sequence I_V(n)*Q_pi).

Links

• Index entries for sequences mentioned in Moon (1987)

Programs

Mathematica

max = 19; q = CoefficientList[ InverseSeries[ Series[-1 + E^(1 + 2*a - E^a), {a, 0, max}], x], x]*Table[x^k, {k, 0, max}] // Total; r = q - Log[1 + x]; v = q + r; ev = (v*q - r)/(1 - v); CoefficientList[ Series[ev, {x, 0, max}], x]*Range[0, max]! (* Jean-François Alcover, Feb 01 2013 *)

Formula

Let Q, R = Q-log(1+x), V=Q+R be the e.g.f.'s for A058379, A058380, A058381 resp. E.g.f.'s for A058475, A058406, A058388 are E_V = (V*Q-R)/(1-V), E_R = E_V/(1+V), E_Q = (E_V+V)/(1+V)-Q.